Microsoft Excel Dose Level Assignment program for Accelerated Titration Designs

S-PLUS Program for the Analysis of Accelerated Titration Designs

Accelerated Titration Designs for Phase I Clinical Trials:

Biometric Research Program staff, in conjunction with others at the NCI and the FDA, have developed new "accelerated titration designs" for phase I clinical trials, along with a dose-toxicity model which can be used to evaluate the toxicity data. The following gives the manuscript reference and abstract, along with brief descriptions of two of the designs, and the dose-toxicity model, which can be used to assign the phase II starting dose, for the use of investigators conducting phase I studies.

Publication:

Simon, R.M., Freidlin, B., Rubinstein, L.V., Arbuck, S., Collins, J., Christian, M., Accelerated titration designs for phase I clinical trials in oncology, Journal of the National Cancer Institute, vol. 89, no. 15, pp. 1138-47 (1997).

Abstract:

Background: Many patients on phase I trials are treated at doses below the biologically active level. Current phase I trials often take a long time to complete and provide little information about inter-patient variability or cumulative toxicity.

Purpose: Our objective was to develop alternative designs for phase I trials that are safe, reduce the number of patients treated at sub-therapeutic dose levels, reduce the duration of the trial and provide more information.

Methods: We fit a stochastic model to data from 20 phase I trials of 9 different drugs. We then simulated new data from the model with the parameters estimated from the actual trials and evaluated the performance of alternative phase I designs on this simulated data. Four designs were evaluated. Design 1 was a conventional design, similar to the commonly used modified Fibonacci, using cohorts of 3-6 patients with 40% dose step increments and no intra-patient dose escalation. Designs 2-4 included only one patient per cohort until one patient experiences dose-limiting toxicity or two patients experience grade 2 toxicity (during their first course of treatment for designs 2-3 or during any course of treatment for design 4). Designs 3 and 4 use 100% dose steps during this initial accelerated phase. After the initial accelerated phase, designs 2-4 resort to standard cohorts of 3-6 patients with 40% dose step increments. Designs 2-4 use intra-patient dose escalation if the worst toxicity is grade 0-1 in the previous course for that patient.

Results: Only 3 of the actual trials showed any evidence of cumulative toxicity. The average number of patients required was reduced from 39.9 for design 1 to 24.4, 20.7 and 21.2 for designs 2, 3 and 4 respectively. The average number of patients who have grade 0-1 toxicity as their worst toxicity over 3 cycles of treatment is 23.3 for design 1 but only 7.9, 3.9 and 4.8 for designs 2, 3 and 4 respectively. The average number of patients with worst toxicity grade 3 increases from 5.5 for design 1 to 6.2, 6.8 and 6.2 for designs 2, 3 and 4 respectively. The average number of patients with worst toxicity grade 4 increases from 1.9 for design 1 to 3.0, 4.3 and 3.2 for designs 2, 3 and 4 respectively. Designs with an accelerated first stage without intra-patient dose escalation also provided substantial reductions in the numbers of under-treated patients but did not reduce the numbers as much as the titration designs. The average number of patients with worst toxicity grade 0-1, 2, 3 and 4 was 10.3, 6.3, 5.2 and 2.2 for design 2 without intra-patient escalation and 7.0, 5.6, 5.2 and 2.8 for design 4 without intra-patient dose escalation.

Conclusion: Accelerated titration designs appear to effectively reduce the number of patients under-treated, speed the completion of phase I trials and provide a substantial increase in the information obtained. These advantages are achieved with some increase in the number of patients experiencing grade 3 and 4 toxicities. Accelerated designs without intra-patient dose escalation also provide major reductions in the number of under-treated patients although they do not provide each patient with the maximum opportunity to receive a dose which may provide therapeutic benefit. We believe that the prospective evaluation of these new designs is justified.

 

Brief Description of Accelerated Titration Design 2:

The dose escalation/de-escalation rules are based on definitions of dose-limiting toxicity (DLT) and of "moderate" toxicity. These definitions may be protocol specific. Dose steps represent 40% increments.

The method used for assignment of dose for the first course of a new patient depends on whether the patient is entered during the early accelerated phase or the latter standard phase of the trial. During the early phase, there is one patient per cohort and the dose for each patient is one dose level (1.4 dose factor) higher than that used for the first course of the previous patient. The accelerated phase ends when one patient experiences DLT during the first course of treatment or when two patients experience "moderate" toxicity during the first course of treatment.

When the accelerated phase ends, the dose assignment for the first course of a new patient is the same as the standard method. Two additional patients are placed on the dose level at which the last new patient was treated, and, subsequently, cohorts of 3-6 patients are started at each dose level. If 0/3 experience first course DLT, the next cohort starts one dose level (1.4 dose factor) higher. If 1/3 experience first course DLT, up to 3 more patients are started at that same dose level. If 2 or more experience first course DLT, no further patients are started at that dose. The largest dose level at which less than 2 patients experience first course DLT is expanded to 6 patients.

The procedure used for intra-patient dose modification is as follows: If a patient has a worst toxicity of DLT during a course, the dose is reduced one dose level for the next course. If the worst toxicity is "moderate" during a course, the dose remains the same for the next course. If worst toxicity is less than "moderate" during a course, the dose is increased one level for the next course.

Brief Description of Accelerated Titration Design 4:

The dose escalation/de-escalation rules are based on definitions of DLT and of "moderate" toxicity. These definitions may be protocol specific. Single dose steps represent 40% increments, but during the early phase of the trial double dose steps (100% increments) are used.

The method used for assignment of dose for the first course of a new patient depends on whether the patient is entered during the early accelerated phase or the latter standard phase of the trial. During the early phase, there is one patient per cohort and the dose for each patient is twice the dose used for the first course of the previous patient. The accelerated phase ends when one patient experiences DLT during any course of treatment or when two different patients experience "moderate" toxicity during any course of treatment. In addition, when the first instance of moderate toxicity is observed, two additional patients must have been treated at that dose, or a higher dose, (during any course) without experiencing moderate or worse toxicity, in order that the accelerated phase continue. This may require the treatment of one or two additional patients at that dose.

When the accelerated phase ends, the dose assignment for the first course of a new patient is the same as for the standard method. Ordinarily, this would mean that two additional patients are placed on the dose level at which the last new patient was treated. We do not suggest reverting to the dose at which DLT (or the higher of the two dose levels at which moderate toxicity) was observed, if this dose is lower than that at which the last new patient was treated. On the other hand, in the case of slow accrual, where individual patients may have been dose escalated and experienced DLT beyond the level at which new patients are treated, we suggest that the accelerated phase may be terminated at the dose level at which the DLT (or the higher of the two dose levels at which moderate toxicity) was observed, rather than reverting to the dose level at which the last new patient was treated. In other words, new patients may continue to receive initial doses double that of the previous new patient, until the dose level is reached at which the DLT (or the second moderate toxicity) was observed. In any case, subsequently, cohorts of 3-6 patients are started at each dose level. If 0/3 experience first course DLT, the next cohort starts one dose level (1.4 dose factor) higher. If 1/3 experience first course DLT, up to 3 more patients are started at that same dose level. If 2 or more experience first course DLT, no further patients are started at that dose. The largest dose level at which < 2 patients experience first course DLT is expanded to 6 patients.

The procedure used for intra-patient dose modification is as follows: If a patient has a worst toxicity of DLT during a course, the dose is reduced one dose level for the next course. If the worst toxicity is "moderate" during a course, the dose remains the same for the next course. If worst toxicity is less than "moderate" during a course, the dose is increased for the next course. The increase is 2 dose levels during the early accelerated phase of the trial, and 1 dose level later.

Choice of the Phase II Starting Dose:

We do not necessarily recommend as the phase II starting dose the highest dose level for which less than 2 patients experience first course DLT. Rather, we suggest that the phase II starting dose be based on the results of fitting all of the toxicity data, including subsequent course toxicity, to the following model for an unobserved continuous variable y_ij representing toxicity level,

y_ij = log(d_ij + aŚD_ij) + b_i + e_ij .

In this model, d_ij represents the dose administered to patient i during course j; D_ij represents the cumulative dose administered to patient i up to, but not including, course j; a represents the relative effect of cumulative prior dose. b_i is normally distributed, with mean 0 and a variance s_b² , representing inter-patient variability. e_ij is normally distributed, with mean 0 and a variance s_e² , representing intra-patient variability. The unobserved variable y_ij translates to the observed discrete toxicity levels by means of three additional parameters, k₁ < k₂ < k₃ , which divide the line into the 4 regions representing "minimal" toxicity (usually grade 0-1), "moderate" toxicity (usually grade 2), DLT, and "unacceptable" toxicity. Thus, the patient toxicity data determines maximum likelihood estimates of the parameters a, s_b² , s_e² , k₁ , k₂ , and k₃ , which yield estimated probabilities of seeing moderate toxicity and DLT at the various dose levels, forming a rational basis for recommending a phase II starting dose. (Drs. Richard Simon and Larry Rubinstein will be available to collaborate on analysis of these accelerated titration design phase I trials.)

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Download the SPlus Program for the Analysis of Accelerated Titration Designs (~ 11 KB)

Instructions to run the Downloaded File:

Software requirements: S-PLUS 3.3 or higher (Under MS Windows). Before running the program, load the functions by typing source('...../ph1atd').  To run the program, type ph1atd( 'inputfile' , 'doselist' ) at the S-PLUS prompt,  where the "inputfile" is an ASCII file which contains the patient data in the following format, one record(line) per course:
    Column 1: patient number
    Column 2: course number
    Column 3: dose
    Column 4: toxicity
(Records should be ordered by patient and course number) and "doselist" is an ASCII file which contains all the doses planned to be used in the trial listed in a single column in ascending order.

Program Output:

• Maximum likelihood estimates of the model parameters
• Confidence intervals for parameters with non-zero MLE, both MLE and CI are sent to the screen and file "ph1atd.out" 
• Graph of probabilities of grade2+, 3+ and 4+ toxicities (for the first course) averaged over the population of patients. (the graph is stored in file "ph1atd1.wmf") 
• Graphs of probabilities of grade2+, 3+ and 4+ toxicities (for the first course) for the patients with beta equal to MLE-SD, MLE and MLE+SD. (the graphs are stored in file "ph1atd2.wmf")

Note: if the MLE of sigma beta is 0 these graphs are not produced